Abstract
In this paper, we introduce a new methodology for socio-economic evaluation with ordinal data, which allows to compute synthetic indicators without variable aggregation, overcoming some of the major problems when classical evaluation procedures are employed in an ordinal setting. In the paper, we describe the methodology step by step, discussing its conceptual and analytical structure. For exemplification purposes, we apply the methodology to real data pertaining to subjective well-being in Italy, for year 2010.
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- 1.
Data are available within a protocol agreement signed by Istat and the University of Florence.
- 2.
In the original dataset, variables are scored as: 4 = “not at all”; 3 = “not much”; 2 = “enough”; 1 = “very”. Codes have been reversed in such a way that increasing scores correspond to increasing satisfaction.
- 3.
We denote this identification function by idn ℓ to remind that it depends upon the linear extension considered.
- 4.
We denote with \(\unlhd _{\ell}\) the order relation in ℓ.
- 5.
More precisely, of a weighted arithmetic mean, but in our case there is no reason to assign different weights to different linear extensions.
- 6.
The terminology is taken by the practice of poverty measurement.
- 7.
The choice of the threshold requires exogenous judgments and assumptions by social scientists and/or policy-makers. It must be noted, however, that the methodology allows for such exogenous information to be introduced in the analysis in a neat and consistent way. One could also add to the analysis judgments on the different relevance of well-being dimensions. Partial order theory, in fact, provides the tools to handle this information in a formal and effective way. We cannot give the details here, but some hints can be found in [6].
- 8.
It is of interest to notice that in standard multivariate approaches, aggregation often exploits interdependencies among variables. Unfortunately, in quality-of-life studies, it turns out that interdependencies may be quite weak. Our approach, which is multidimensional in nature, overcomes this issue by addressing the evaluation problem as a problem of multidimensional comparison.
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Fattore, M., Maggino, F., Arcagni, A. (2016). Non-aggregative Assessment of Subjective Well-Being. In: Alleva, G., Giommi, A. (eds) Topics in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-27274-0_20
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DOI: https://doi.org/10.1007/978-3-319-27274-0_20
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